Extensional constructs in intensional type theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
London u.a.
Springer
1997
|
| Series: | CPHC/BCS distinguished dissertations
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 214 S. |
| ISBN: | 3540761217 |
Staff View
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| 100 | 1 | |a Hofmann, Martin |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Extensional constructs in intensional type theory |c Martin Hofmann |
| 264 | 1 | |a London u.a. |b Springer |c 1997 | |
| 300 | |a XII, 214 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 0 | |a CPHC/BCS distinguished dissertations | |
| 650 | 4 | |a Automatic theorem proving | |
| 650 | 4 | |a Functional programming (Computer science) | |
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Record in the Search Index
| _version_ | 1807505395827081216 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
PREFACE
.
V
1.
INTRODUCTION
.
1
1.1
DEFINITIONAL
AND
PROPOSITIONAL
EQUALITY
.
1
1.2
EXTENSIONAL
CONSTRUCTS
.
4
1.3
METHOD
.
5
1.3.1
THE
USE
OF
CATEGORICAL
MODELS
.
6
1.3.2
SYNTACTIC
MODELS
.
6
1.4
APPLICATIONS
.
8
1.4.1
APPLICATION
TO
MACHINE-ASSISTED
THEOREM
PROVING
.
8
1.5
OVERVIEW
.
9
2.
SYNTAX
AND
SEMANTICS
OF
DEPENDENT
TYPES
.
13
2.1
SYNTAX
FOR
A
CORE
CALCULUS
.
13
2.1.1
RAW
SYNTAX
.
14
2.1.2
JUDGEMENTS
.
14
2.1.3
NOTATION
.
17
2.1.4
DERIVED
RULES
AND
META-THEORETIC
PROPERTIES
.
18
2.2
HIGH-LEVEL
SYNTAX
.
19
2.2.1
TELESCOPES
.
19
2.2.2
ELEMENTS
OF
TELESCOPES
AND
CONTEXT
MORPHISMS
.
19
2.2.3
DEFINITIONS
AND
SUBSTITUTION
.
20
2.3
FURTHER
TYPE
FORMERS
.
21
2.3.1
UNIT
TYPE
.
21
2.3.2
27-TYPES
.
22
2.3.3
FUNCTION
AND
CARTESIAN
PRODUCT
TYPES
.
22
2.3.4
THE
CALCULUS
OF
CONSTRUCTIONS
.
22
2.3.5
UNIVERSES
.
23
2.3.6
QUOTIENT
TYPES
.
24
2.4
ABSTRACT
SEMANTICS
OF
TYPE
THEORY
.
24
2.4.1
SYNTACTIC
CATEGORIES
WITH
ATTRIBUTES
.
25
2.4.2
TYPE
CONSTRUCTORS
.
34
2.5
INTERPRETING
THE
SYNTAX
.
45
2.5.1
PARTIAL
INTERPRETATION
.
45
2.5.2
SOUNDNESS
OF
THE
INTERPRETATION
.
46
2.6
DISCUSSION
AND
RELATED
WORK
.
53
3.
SYNTACTIC
PROPERTIES
OF
PROPOSITIONAL
EQUALITY
.
55
3.1
INTENSIONAL
TYPE
THEORY
.
55
3.1.1
SUBSTITUTION
.
55
3.1.2
UNIQUENESS
OF
IDENTITY
.
57
3.1.3
FUNCTIONAL
EXTENSIONALITY
.
59
3.2
EXTENSIONAL
TYPE
THEORY
.
61
3.2.1
COMPARISON
WITH
TROELSTRA
'
S
PRESENTATION
.
62
3.2.2
UNDECIDABILITY
OF
EXTENSIONAL
TYPE
THEORY
.
62
3.2.3
INTERPRETING
EXTENSIONAL
TYPE
THEORY
IN
INTENSIONAL
TYPE
THEORY
.
64
3.2.4
AN
EXTENSION
OF
TT/
FOR
WHICH
THE
INTERPRETATION
IN
TT
E
IS
SURJECTIVE
.
66
3.2.5
CONSERVATIVITY
OF
TT
B
OVER
TT/
.
68
3.2.6
DISCUSSION
AND
EXTENSIONS
.
77
3.2.7
CONSERVATIVITY
OF
QUOTIENT
TYPES
AND
FUNCTIONAL
EXTEN
SIONALITY
.
84
3.3
RELATED
WORK
.
86
4.
PROOF
IRRELEVANCE
AND
SUBSET
TYPES
.
89
4.1
THE
REFINEMENT
APPROACH
.
.89
4.2
THE
DELIVERABLES
APPROACH
.
91
4.3
THE
DELIVERABLES
MODEL
.
'
.
92
4.3.1
CONTEXTS
.
92
4.3.2
FAMILIES
OF
SPECIFICATIONS
.
93
4.3.3
SECTIONS
OF
SPECIFICATIONS
(DELIVERABLES)
.
94
4.4
MODEL
CHECKING
WITH
LEGO
.
94
4.4.1
RECORDS
IN
LEGO
.
95
4.4.2
DELIVERABLES
IN
LEGO
.
95
4.5
TYPE
FORMERS
IN
THE
MODEL
D
.
97
4.5.1
DEPENDENT
PRODUCTS
.
97
4.5.2
DEPENDENT
SUMS
.
98
4.5.3
NATURAL
NUMBERS
.
100
4.5.4
THE
TYPE
OF
PROPOSITIONS
.
100
4.5.5
PROOF
IRRELEVANCE
.
103
4.5.6
UNIVERSES
.
104
4.6
SUBSET
TYPES
.
105
4.6.1
SUBSET
TYPES
WITHOUT
IMPREDICATIVITY
.
106
4.6.2
A
NON-STANDARD
RULE
FOR
SUBSET
TYPES
.
106
4.7
REINTERPRETATION
OF
THE
EQUALITY
JUDGEMENT
.
ILL
4.8
RELATED
WORK
.
112
5.
EXTENSIONALITY
AND
QUOTIENT
TYPES
.
115
5.1
THE
SETOID
MODEL
.
115
5.1.1
CONTEXTS
OF
SETOIDS
.
116
5.1.2
IMPLEMENTING
THE
SETOID
MODEL
SO
IN
LEGO
.
119
5.1.3
TYPE
FORMERS
IN
THE
SETOID
MODEL
.
119
5.1.4
PROPOSITIONS
.
120
5.1.5
QUOTIENT
TYPES
.
125
5.1.6
INTERPRETATION
OF
QUOTIENT
TYPES
IN
SO
.
126
5.1.7
A
CHOICE
OPERATOR
FOR
QUOTIENT
TYPES
.
129
5.1.8
TYPE
DEPENDENCY
AND
UNIVERSES
.
132
5.2
THE
GROUPOID
MODEL
.
135
5.2.1
GROUPOIDS
.
136
5.2.2
INTERPRETATION
OF
TYPE
FORMERS
.
142
5.2.3
UNIQUENESS
OF
IDENTITY
.
146
5.2.4
PROPOSITIONAL
EQUALITY
AS
ISOMORPHISM
.
147
5.3
A
DEPENDENT
SETOID
MODEL
.
148
5.3.1
FAMILIES
OF
SETOIDS
.
150
5.3.2
DEPENDENT
PRODUCT
.
153
5.3.3
THE
IDENTITY
TYPE
.
154
5.3.4
INDUCTIVE
TYPES
.
156
5.3.5
QUOTIENT
TYPES
.
158
5.4
DISCUSSION
AND
RELATED
WORK
.
160
6.
APPLICATIONS
.
163
6.1
TARSKI
'
S
FIXPOINT
THEOREM
.
164
6.1.1
DISCUSSION
.
167
6.2
STREAMS
IN
TYPE
THEORY
.
167
6.3
CATEGORY
THEORY
IN
TYPE
THEORY
.
171
6.3.1
CATEGORIES
IN
SO
.
172
6.3.2
CATEGORIES
IN
SI
.
174
6.3.3
DISCUSSION
.
175
6.4
ENCODING
OF
THE
COPRODUCT
TYPE
.
176
6.4.1
DEVELOPMENT
IN
THE
SETOID
MODELS
.
177
6.5
SOME
BASIC
CONSTRUCTIONS
WITH
QUOTIENT
TYPES
.
178
6.5.1
CANONICAL
FACTORISATION
OF
A
FUNCTION
.
178
6.5.2
SOME
CATEGORICAL
PROPERTIES
OF
SO
.
180
6.5.3
SUBSETS
AND
QUOTIENTS
.
180
6.5.4
SATURATED
SUBSETS
.
181
6.5.5
ITERATED
QUOTIENTS
.
182
6.5.6
QUOTIENTS
AND
PRODUCTS
.
182
6.5.7
QUOTIENTS
AND
FUNCTION
SPACES
.
183
6.6
S
IS
CO-CONTINUOUS
-
INTENSIONALLY
.
184
6.6.1
PARAMETRISED
LIMITS
OF
W-CHAINS
.
184
6.6.2
DEVELOPMENT
IN
TTG
.
186
6.6.3
DEVELOPMENT
IN
TT;
.
186
7.
CONCLUSIONS
AND
FURTHER
WORK
.
189
APPENDIX
A.
LEGO
CONTEXT
APPROXIMATING
SO
.
191
A.L
EXTENSIONALITY
AXIOMS
.
191
A.
2
QUOTIENT
TYPES
.
191
A.
3
FURTHER
AXIOMS
.
192
APPENDIX
B.
SYNTAX
.
193
APPENDIX
C.
A
GLOSSARY
OF
TYPE
THEORIES
.
201
APPENDIX
D.
INDEX
OF
SYMBOLS
.
203
INDEX
.
212 |
| any_adam_object | 1 |
| author | Hofmann, Martin |
| author_facet | Hofmann, Martin |
| author_role | aut |
| author_sort | Hofmann, Martin |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Book |
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| id | DE-604.BV011205501 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-16T01:24:31Z |
| institution | BVB |
| isbn | 3540761217 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007516124 |
| oclc_num | 36104250 |
| open_access_boolean | |
| owner | DE-384 DE-91G DE-BY-TUM DE-634 |
| owner_facet | DE-384 DE-91G DE-BY-TUM DE-634 |
| physical | XII, 214 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series2 | CPHC/BCS distinguished dissertations |
| spelling | Hofmann, Martin Verfasser aut Extensional constructs in intensional type theory Martin Hofmann London u.a. Springer 1997 XII, 214 S. txt rdacontent n rdamedia nc rdacarrier CPHC/BCS distinguished dissertations Automatic theorem proving Functional programming (Computer science) Type theory Martin-Löf-Typentheorie (DE-588)4347541-3 gnd rswk-swf Martin-Löf-Typentheorie (DE-588)4347541-3 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007516124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hofmann, Martin Extensional constructs in intensional type theory Automatic theorem proving Functional programming (Computer science) Type theory Martin-Löf-Typentheorie (DE-588)4347541-3 gnd |
| subject_GND | (DE-588)4347541-3 |
| title | Extensional constructs in intensional type theory |
| title_auth | Extensional constructs in intensional type theory |
| title_exact_search | Extensional constructs in intensional type theory |
| title_full | Extensional constructs in intensional type theory Martin Hofmann |
| title_fullStr | Extensional constructs in intensional type theory Martin Hofmann |
| title_full_unstemmed | Extensional constructs in intensional type theory Martin Hofmann |
| title_short | Extensional constructs in intensional type theory |
| title_sort | extensional constructs in intensional type theory |
| topic | Automatic theorem proving Functional programming (Computer science) Type theory Martin-Löf-Typentheorie (DE-588)4347541-3 gnd |
| topic_facet | Automatic theorem proving Functional programming (Computer science) Type theory Martin-Löf-Typentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007516124&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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